A129701 Difference between successive primes cubed: a(n) = prime(n+1)^3 - prime(n)^3.

19, 98, 218, 988, 866, 2716, 1946, 5308, 12222, 5402, 20862, 18268, 10586, 24316, 45054, 56502, 21602, 73782, 57148, 31106, 104022, 78748, 133182, 207704, 117628, 62426, 132316, 69986, 147868, 605486, 199708, 323262, 114266, 622330, 135002

Offset: 1

Author

Ben Paul Thurston, Jun 01 2007

Keywords

• nonn

Examples

			a(3) because the fourth prime is 7, cubed 343, the third prime is 5, cubed 125, 343-125=218.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A030078 (cubes of primes).

Programs

Magma

[NthPrime(n+1)^3 - NthPrime(n)^3: n in [1..40]]; // G. C. Greubel, May 19 2019

Maple

last:=8;for i from 3 to 30 do > while isprime(i)=false do > i:=i + 1; > end do; > r:= i^3 - last; > last:=i^3; > end do;

Mathematica

Table[Prime[n+1]^3 - Prime[n]^3, {n, 1, 40}] (* Stefan Steinerberger, Jun 05 2007 *)
Last[#]-First[#]&/@(Partition[Prime[Range[40]],2,1]^3) (* Harvey P. Dale, Oct 13 2012 *)

PARI

{a(n) = prime(n+1)^3 - prime(n)^3}; \\ G. C. Greubel, May 19 2019

Sage

[nth_prime(n+1)^3 - nth_prime(n)^3 for n in (1..40)] # G. C. Greubel, May 19 2019

Formula

a(n) = A030078(n+1) - A030078(n). - Michel Marcus, Sep 04 2013

Extensions

More terms from Stefan Steinerberger, Jun 05 2007